A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.
Mots-clés : constitutive law, finite element method, biological tissue, hyperelasticity, nonlinear partial differential equations, anisotropic material
@article{M2AN_2003__37_4_725_0,
author = {Bourdarias, Christian and Gerbi, St\'ephane and Ohayon, Jacques},
title = {A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {725--739},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003044},
mrnumber = {2018440},
zbl = {1070.74045},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003044/}
}
TY - JOUR AU - Bourdarias, Christian AU - Gerbi, Stéphane AU - Ohayon, Jacques TI - A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 725 EP - 739 VL - 37 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003044/ DO - 10.1051/m2an:2003044 LA - en ID - M2AN_2003__37_4_725_0 ER -
%0 Journal Article %A Bourdarias, Christian %A Gerbi, Stéphane %A Ohayon, Jacques %T A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 725-739 %V 37 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003044/ %R 10.1051/m2an:2003044 %G en %F M2AN_2003__37_4_725_0
Bourdarias, Christian; Gerbi, Stéphane; Ohayon, Jacques. A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates. ESAIM: Modélisation mathématique et analyse numérique, Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 725-739. doi : 10.1051/m2an:2003044. http://archive.numdam.org/articles/10.1051/m2an:2003044/
[1] , On the local reaction of the arterial wall to changes of internal pressure. J. Physiol. London 28 (1902) 220-231.
[2] , and, Algorithm 698: DCUHRE: An adaptive multidimensional integration routine for a vector of integrals. ACM Trans. Math. Softw. 17 (1991) 452-456. | Zbl
[3] ,,, and, Dependance of local left ventricular wall mechanics on myocardial fiber orientation: a model study. J. Biomech. 25 (1992) 1129-1140.
[4] , The finite element method for elliptic problems, Vol. 4 of Studies in Mathematics and its Applications. North-Holland, Amsterdam-New York (1980). | MR | Zbl
[5] ,,,, and, A three-dimensional finite element method for large elastic deformations of ventricular myocardium: Part I. Cylindrical and spherical polar coordinates. ASME J. Biomech. Eng. 118 (1996) 452-463.
[6] and, Augmented lagrangian and operator-splitting methods in nonlinear mechanics. SIAM, Philadelphia, PA (1989). | MR | Zbl
[7] and, A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. J. Biomech. Eng. 120 (1998) 504-517.
[8] , Introduction to the mechanics of a continuous medium. Prentice-Hall (1969).
[9] ,, and, Large scale finite element analysis of the beating heart. Crit. Rev. Biomed. Eng. 20 (1992) 427-449.
[10] , and, User Guide for MINPACK-1. Technical Report ANL-80-74, Argonne National Laboratory (March 1980).
[11] , Finite elements of nonlinear continua. McGraw-Hill, New York (1972). | Zbl
[12] and, Effects of collagen microstructure on the mechanics of the left ventricle. Biophys. J. 54 (1988) 1077-1088.
[13] , A hybrid method for nonlinear equations, in Numerical methods for nonlinear algebraic equations, P. Rabinowitz Ed. Gordon and Breach, New York (1970) 87-114. | Zbl
[14] and, Numerical approximation of partial differential equations, Vol. 23 of Springer Series in Computational Mathematics. Springer Verlag, Berlin (1994). | MR | Zbl
[15] , Mechanoreception by the vascular wall. Futura Publishing Company, Inc. (1993).
[16] , On a nonlinear theory for muscle shells: Part II. Application to the beating left ventricle. J. Biomech. Eng. 113 (1991) 63-71.
[17] , and, Interaction fluide-structure active : écoulement artériel. C.R. Acad. Sci. Paris 324 (1997) 37-45. | Zbl
[18] , and, Regional septal dysfunction in a three-dimensional computational model of focal myofiber dissaray. Am. J. Physiol. Heart Circ. Physiol. 281 (2001) 506-514.
[19] and, A class of indefinite dogleg path mehods for unconstrained minimization. SIAM J. Optim. 9 (1999) 646-667. | Zbl
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